Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 9x - 1$ and $ KL = 3x + 35$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {9x - 1} = {3x + 35}$ Solve for $x$ $ 6x = 36$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 9({6}) - 1$ $ KL = 3({6}) + 35$ $ JK = 54 - 1$ $ KL = 18 + 35$ $ JK = 53$ $ KL = 53$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {53} + {53}$ $ JL = 106$